\title{Home}

\subsection{A library for probabilistic modeling, inference, and criticism.}

Edward is a Python library for probabilistic modeling, inference, and
criticism. It is a testbed for fast experimentation and research with
probabilistic models, ranging from classical hierarchical models on
small data sets to complex deep probabilistic models on large data
sets. Edward fuses three fields: Bayesian statistics and machine
learning, deep learning, and probabilistic programming.

It supports \textbf{modeling} with

\begin{itemize}
\item Directed graphical models
\item Neural networks (via libraries such as
  \href{https://www.tensorflow.org/api_docs/python/tf/layers}{\texttt{tf.layers}}
  and
  \href{http://keras.io}{Keras})
\item Implicit generative models
\item Bayesian nonparametrics and probabilistic programs
\end{itemize}

It supports \textbf{inference} with

\begin{itemize}
\item Variational inference
  \begin{itemize}
    \item Black box variational inference
    \item Stochastic variational inference
    \item Generative adversarial networks
    \item Maximum a posteriori estimation
  \end{itemize}
\item Monte Carlo
  \begin{itemize}
    \item Gibbs sampling
    \item Hamiltonian Monte Carlo
    \item Stochastic gradient Langevin dynamics
  \end{itemize}
\item Compositions of inference
  \begin{itemize}
    \item Expectation-Maximization
    \item Pseudo-marginal and ABC methods
    \item Message passing algorithms
  \end{itemize}
\end{itemize}

It supports \textbf{criticism} of the model and inference with

\begin{itemize}
\item Point-based evaluations
\item Posterior predictive checks
\end{itemize}

Edward is built on
\href{https://www.tensorflow.org}{TensorFlow}. It enables features such
as computational graphs, distributed training, CPU/GPU integration,
automatic differentiation, and visualization with TensorBoard.

\subsubsection{Authors}

Edward is led by \href{http://dustintran.com}{Dustin Tran} with
guidance by \href{http://www.cs.columbia.edu/~blei/}{David Blei}.
See the \href{https://github.com/blei-lab/edward/graphs/contributors}
{full list of contributors}.

We are open to collaboration, and welcome
researchers and developers to contribute. Check out the
\href{/contributing}{contributing page} for how to improve Edward's software.
For broader research discussion, check out the
\href{https://discourse.edwardlib.org}{Forum}.

Edward has benefited enormously from the helpful feedback and advice
of many individuals: Jaan Altosaar, Eugene Brevdo, Allison Chaney,
Joshua Dillon, Matthew Hoffman, Kevin Murphy, Rajesh Ranganath, Rif
Saurous, and other members of the Blei Lab, Google Brain, and Google
Research.

\subsubsection{Citation}

There are several articles to cite for Edward;
also see Edward's \href{/license}{license page}.

The following article describes the API of Edward. It bundles the
website's documentation as a PDF.
We recommend citing this article as a general default.

\begin{quote}
Dustin Tran, Alp Kucukelbir, Adji B. Dieng, Maja Rudolph, Dawen Liang,
and David M. Blei.
2016.
\href{https://arxiv.org/abs/1610.09787}
{\emph{Edward: A library for probabilistic modeling, inference, and criticism.}}
arXiv preprint arXiv:1610.09787.
\end{quote}

\begin{lstlisting}[class=JSON]
@article{tran2016edward,
  author = {Dustin Tran and Alp Kucukelbir and Adji B. Dieng and Maja Rudolph and Dawen Liang and David M. Blei},
  title = {{Edward: A library for probabilistic modeling, inference, and criticism}},
  journal = {arXiv preprint arXiv:1610.09787},
  year = {2016}
}
\end{lstlisting}

The following article describes the algorithmic foundations of Edward,
with a \href{/iclr2017}{companion webpage here}.
We recommend citing this article if you are discussing Edward's
design and methodology.

\begin{quote}
Dustin Tran, Matthew D. Hoffman, Rif A. Saurous, Eugene Brevdo, Kevin
Murphy, and David M. Blei.
2017.
\href{https://arxiv.org/abs/1701.03757}{\emph{Deep Probabilistic Programming.}}
International Conference on Learning Representations.
\end{quote}

\begin{lstlisting}[class=JSON]
@inproceedings{tran2017deep,
  author = {Dustin Tran and Matthew D. Hoffman and Rif A. Saurous and Eugene Brevdo and Kevin Murphy and David M. Blei},
  title = {Deep probabilistic programming},
  booktitle = {International Conference on Learning Representations},
  year = {2017}
}
\end{lstlisting}
